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# Is There a Role for Mathematics in Food Security?

What is “food security”? According to the World Health Organization, food security exists when all people at all times have access to sufficient, safe, nutritious food to maintain a healthy and active life. Food security is a complex issue with important implications for public health, sustainable economic development, the environment, and trade. The Obama administration has declared food security a federal priority area, so here is another opportunity for our community to apply its modeling and computational expertise. The question is: Where is the mathematics, and if there is mathematics in food security, how can we participate?

To get the discussion started, and possibly define a research agenda, the American Institute of Mathematics (AIM) sponsored a workshop on Multiscale Modeling of the Food System at its San Jose facility in California, April 27-30, 2015. Organized by John Ingram (Environmental Change Institute, Oxford, UK) and Mary Lou Zeeman (Bowdoin College, US), the workshop attracted economists, social scientists, food and nutritional specialists, mathematicians interested in modeling complex systems, and data specialists.

The first thing to note is that food security involves more than food production; it also has to do with food availability, food accessibility, and food use. The entire set of activities by which calories and nutrients are grown, harvested, traded, processed, transported, stored, sold, prepared, and eventually consumed is called the food system, as illustrated in Figure 1. Clearly, it is a complex system: it has many components; all the components interact;  the interactions are often nonlinear; and there are numerous feedback loops, most of which are poorly understood and which can be positive or negative, depending on the state of the system.

Figure 1. The Food System. The top box represents food system outcomes. The pale blue "Consumers," "Food Chain Actors," and "Producers" boxes represent food system activities. Darker blue boxes represent modeling approaches for separate components of the food system. Darker blue arrows represent inherent feedbacks. Reproduced from [1].

These observations suggest that the food system could be modeled as a network. For example, the nodes can represent nutrients and the edges (directed links) processes or activities along the food chain, with external forces (climate change, droughts, etc.) affecting the outcome of certain processes and activities. Bayesian networks are often used to model a domain containing uncertainty, and therefore provide a tool for reasoning under uncertainty. Uncertainties can arise due to an imperfect understanding of the system, incomplete knowledge of the state of the system, randomness in the mechanisms governing the behavior of the system, or any combination of these. Mathematicians have developed techniques for studying the dynamics of networks, given its topology. These techniques can be applied or adapted to study food security models and could provide information on the relevance or irrelevance of certain components of the system.

The workshop at AIM offered a hands-on approach. Since most of the mathematicians had never been exposed to the problems of food security, the activities focused on three specific questions, each relevant to a particular aspect of food security in the US:

1. What currently drives dietary inequality in the US?
2. What are robust transformative strategies to promote urban food production, healthy diets, and social capital?
3. How can we design a market system  so that food prices embody the externalities (social and environmental costs) of food choices?

These questions were selected through a voting process from a longer list of 14 questions suggested by the participants on the first day of the workshop (see sidebar).

The (often lively) discussions yielded insight into the nature of the questions, relevant metrics, the availability of quantitative data (or lack thereof), and the modeling options. Clear cross-cutting themes emerged: interdisciplinary research, hybrid modeling, data mining, etc. Also, it soon became apparent that there is no hope for a one-size-fits all approach to the questions. For example, the discussions on the incorporation of externalities in food prices (question 3) brought to light the fact that products as diverse as corn and shrimp pose very different challenges: while the government has significant authority to regulate the price of a domestic staple product like corn, it has very little control over the externalities of shrimp, which is mostly produced abroad and imported.

Most interesting, workshop participants identified a long list of exploratory projects suitable for research with graduate and undergraduate students, including summarizing and visualizing data sets; constructing heat maps representing particular indices from nutrition databases; designing  agent-based models to simulate behavior and choice processes; coupling conceptual dynamical-systems models, agent-based models, and Bayesian network models; and designing an object-oriented framework for modeling the food system.

The AIM workshop was the start of an effort to bring a new area of applications to the attention of the mathematics and computational science communities. More needs to be done. Food security will be one of the themes at the inaugural conference of the newly formed SIAM Activity Group on Mathematics of Planet Earth (SIAG/MPE), which will be held in Philadelphia, September 30-October 2, 2016.

References
[1] Acharya, T., et al. (2014, June). Assessing Sustainable Nutrition Security: The Role of Food Systems. The International Life Sciences Institute, Research Foundation, Center for Integrated Modeling of Sustainable Agriculture and Nutrition, Washington, DC.

Hans Kaper, founding chair of SIAG/MPE and editor-in-chief of SIAM News, is an adjunct professor of mathematics at Georgetown University.